Answer:
The escape speed on the other planet is V
Explanation:
Escape velocity V = √2GM/R where M = mass of planet and R = radius of planet. G = gravitational constant
Let V₁ and V₂ be the escape speeds on planet one and two respectively.
if V₁ = √2GM₁/R₁ and V₂ = √2GM₂/R₂ and M₂ = 2M₁ and R₂ = 2R₁ (since it is twice the size of the first planet)
V₂ = √2GM₂/R₂ = V₂ = √(2G × 2M₁/2R₁) = √2GM₁/R₁ = V₁ = V
So the escape speed on the other planet is V
Answer:
Explanation:
Given:
M₂ = 2 × M₁
R₂ = 2 × R₁
Escape velocity, V = √2GM/R
Let V₁ and V₂ be the escape velocity of the first and second planet respectively.
V₁ = √2GM₁/R₁
V₂ = √2GM₂/R₂
Equating V₁ and V₂, we have:
(V₁)^2 × R₁ /(2 × M₁) = (V₂)^2 × M₂/(2 × R₂)
(V₁)^2 × R₁ /(2 × M₁) = (V₂)^2 × 2 × R₁ /(2 × 2 × M₁)
(V₁)^2 = (V₂)^2 × (2 × M₁)/R₁ × 2 × R₁/(4 × M₁)
(V₁)^2 = (V₂)^2
V₁ = V₂
